Formula:KLS:14.10:97

<< Formula:KLS:14.10:96

formula in Continuous q-Jacobi: Special cases

Formula:KLS:14.10:98 >>

${\displaystyle{\displaystyle{\displaystyle P_{n}\!\left(x|q\right)=\frac{2^{n}q^{\frac{1}{4}n}\left(q^{\frac{1}{2}};q\right)_{n}}{\left(q;q\right)_{n}}{\widehat{P}}_{n}\!\left(x\right)}}}$

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Symbols List

${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : continuous ${\displaystyle{\displaystyle{\displaystyle q}}}$-Legendre polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsqLegendre
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle{\widehat{P}}_{n}}}}$ : monic continuous ${\displaystyle{\displaystyle{\displaystyle q}}}$-Legendre polynomial : http://drmf.wmflabs.org/wiki/Definition:monicctsqLegendre

Bibliography

Equation in Section 14.10 of KLS.

URL links

We ask users to provide relevant URL links in this space.

<< Formula:KLS:14.10:96

formula in Continuous q-Jacobi: Special cases

Formula:KLS:14.10:98 >>